MA3: Shape, Space and Measures
Properties of Shape
Understanding shapes
Properties of position and movement
Measuring
Measures
Level 1
When working with 2-D and 3-D shapes, pupils use everyday language to describe properties and positions. They measure and order objects using direct comparison and order events.
• use everyday language to describe properties of 2-D and 3-D
shapes, e.g.
- sort shapes and say how they have selected them
- use properties such as large, small, triangles, roll, stack
- begin to refer to some features of shapes such as side and corner
- begin to name the shapes they use in the context of an activity
• use everyday language to describe positions of 2-D and 3-D
shapes
- respond to and use positional language, e.g. ‘behind’, under’, ‘on top
of’, ‘next to’, ‘in between’…
- respond to and use directional language in talk about objects and
movement, e.g. ‘forwards’, ‘backwards’, ‘turn’
• measure and order objects using direct comparison
- compare lengths directly and put them in order
- respond to and use the language of comparison: longer, longest,
shorter, shortest, more, less, heavier, lighter
- check which of two objects is heavier/lighter and begin to put three
objects into order
- find objects that are longer/shorter than a metre, heavier/lighter than
500 grams, hold more/less than 1 litre
• order events
- order everyday events and describe the sequence
- use the vocabulary of time including days of the week
- read the time on an analogue clock at the hour and begin to know the
half hour
Level 2
Pupils use mathematical names for common 3-D and 2-D shapes and describe their properties, including numbers of sides and corners. They distinguish between straight and turning movements, understand angle as a
measurement of turn, and recognise right angles in turns. They begin to use everyday non-standard and standard units to measure length and mass.
• use mathematical names for common 3-D and 2-D shapes, e.g.
- identify 2-D and 3-D shapes from pictures of them in different
orientations, e.g. square, triangle, hexagon, pentagon, octagon, cube,
cylinder, sphere, cuboid, pyramid
• describe their properties, including numbers of sides and
corners, e.g.
- make and talk about shapes referring to properties and features such
as edge, face, corner
- sort 2-D and 3-D shapes according to a single criterion, e.g. shapes
that are pentagons or shapes with a right angle
- visualise frequently used 2-D and 3-D shapes
- begin to understand the difference between shapes with two
dimensions and those with three
- recognise properties that are the same even when a shape is
enlarged, e.g. comparing squares, circles, similar triangles, cubes or
spheres of different sizes
• describe the position of objects, e.g.
- use ordinal numbers (first, second, third…) to describe the position of
objects in a row or when giving directions
- recognise and explain that a shape stays the same even when it is
held up in different orientations
• distinguish between straight and turning movements
- distinguish between left and right and between clockwise and
anticlockwise and use these when giving directions
- instruct a programmable robot, combining straight-line movements
and turns, to move along a defined path or reach a target destination
• recognise right angles in turns
• understand angle as a measurement of turn
- make whole turns, half-turns and quarter-turns
• begin to use everyday non-standard and standard units to
measure length and mass
- begin to understand that numbers can be used not only to count
discrete objects but also to describe continuous measures, e.g. length
- know which measuring tools to use to find, e.g. how much an object
weighs, how tall a child is, how long it takes to run around the edge of
the playground, how much water it takes to fill the water tray
- read scales to the nearest labelled division
• begin to use a wider range of measures
- make and use a ‘right angle checker’
- use a time line to order daily events and ordinal numbers (first,
second, third…) to describe the order of some regular events
Level 3
Pupils classify 3-D and 2-D shapes in various ways using mathematical properties such as reflective symmetry for 2-D shapes. They use non-standard units, standard metric units of length, capacity and mass, and standard
units of time, in a range of contexts.
• classify 3-D and 2-D shapes in various ways using mathematical
properties such as reflective symmetry for 2-D shapes, e.g.
- sort objects and shapes using more than one criterion, e.g. pentagon,
not pentagon and all edges the same length/not the same length
- sort the shapes which have all edges the same length and all angles
the same size from a set of mixed shapes and begin to understand
the terms ‘regular’ and ‘irregular’
- recognise right angles in shapes in different orientations
- recognise angles which are bigger/smaller than 90° and begin to know
the terms ‘obtuse’ and ‘acute’
- recognise right-angled and equilateral triangles
- demonstrate that a shape has reflection symmetry by folding and
recognise when a shape does not have a line of symmetry
- recognise common 3-D shapes, e.g. triangular prism, square-based
pyramid
- relate 3-D shapes to drawings and photographs of them, including
from different viewpoints
• begin to recognise nets of familiar 3-D shapes, e.g. cube, cuboid,
triangular prism, square-based pyramid
• recognise shapes in different orientations
• reflect shapes, presented on a grid, in a vertical or horizontal
mirror line, e.g.
- reflect a shape even if the shape is at 45° to the mirror line, touching
the line or not
- begin to reflect simple shapes in a mirror line presented at 45°
• describe position and movement, e.g.
- use terms such as left/right, clockwise/anticlockwise, quarter turn/90°
to give directions along a route
• use non-standard units and standard metric units of length,
capacity and mass in a range of contexts, e.g.
- measure a length to the nearest 1/2 cm
- read simple scales, e.g. increments of 2, 5 or 10
• use standard units of time, e.g.
- read a 12-hour clock and generally calculate time durations that do
not go over the hour
• use a wider range of measures, e.g.
- begin to understand area as a measure of surface and perimeter as a
measure of length
- begin to find areas of shapes by counting squares and explain
answers as a number of squares even if not using standard units such
as cm2 or m2
- recognise angles as a measure of turn and know that one whole turn
is 360 degrees
Properties of Shape
Understanding shapes
Properties of position and movement
Measuring
Measures
Level 4
Pupils make 3-D mathematical models by linking given faces or edges, draw common 2-D shapes in different orientations on grids. They reflect simple shapes in a mirror line. They choose and use appropriate units and
instruments, interpreting, with appropriate accuracy, numbers on a range of measuring instruments. They find perimeters of simple shapes and find areas by counting squares.
• use the properties of 2-D and 3-D shapes, e.g.
- recognise and name most quadrilaterals, e.g. trapezium,
parallelogram, rhombus
- recognise right-angled, equilateral, isosceles and scalene triangles
- recognise an oblique line of symmetry in a shape
- use mathematical terms such as horizontal, vertical, congruent (same
size, same shape)
- understand properties of shapes, e.g. why a square is a special
rectangle
- visualise shapes and recognise them in different orientations
• make 3-D models by linking given faces or edges
• draw common 2-D shapes in different orientations on grids, e.g.
- complete a rectangle which has two sides drawn at an oblique angle
to the grid
• reflect simple shapes in a mirror line, e.g.
- use a grid to plot the reflection in a mirror line presented at 45° where
the shape touches the line or not
- begin to use the distance of vertices from the mirror line to reflect
shapes more accurately
• begin to rotate a simple shape or object about its centre or a
vertex
• translate shapes horizontally or vertically
• choose and use appropriate units and instruments
• interpret, with appropriate accuracy, numbers on a range of
measuring instruments, e.g.
- measure a length using mm, to within 2 mm
- measure and draw acute and obtuse angles to the nearest 5º, when
one edge is horizontal/vertical
• find perimeters of simple shapes and find areas by counting
squares, e.g.
- use the terms ‘area’ and ‘perimeter’ accurately and consistently
- find areas by counting squares and part squares
- begin to find the area of shapes that need to be divided into
rectangles
- use ‘number of squares in a row times number of rows’ to find the
area of a rectangle
• use units of time, e.g.
- calculate time durations that go over the hour
- read and interpret timetables
Level 5
When constructing models and when drawing or using shapes, pupils measure and draw angles to the nearest degree, and use language associated with angle. Pupils know the angle sum of a triangle and that of angles at a
point. They identify all the symmetries of 2-D shapes. They know the rough metric equivalents of imperial units still in daily use and convert one metric unit to another. They make sensible estimates of a range of measures in
relation to everyday situations. Pupils understand and use the formula for the area of a rectangle.
• use a wider range of properties of 2-D and 3-D shapes, e.g.
- understand ‘parallel’ and begin to understand ‘perpendicular’ in
relation to edges or faces
- classify quadrilaterals, including trapezium and kite, using their
properties, e.g. number of parallel sides
- reason about special triangles and quadrilaterals, e.g. given the
perimeter and one side of an isosceles triangle, find both possible
triangles
- draw a parallelogram or trapezium of a given area on a square grid
- given the coordinates of three vertices of a parallelogram, find the
fourth
• know and use the angle sum of a triangle and that of angles at a
point, e.g.
- calculate ‘missing angles’ in triangles, including isosceles triangles or
right-angled triangles, when only one/one other angle is given
- calculate angles on a straight line or at a point such as the angle
between the hands of a clock, or intersecting diagonals at the centre
of a regular hexagon
• identify all the symmetries of 2-D shapes (for rotation symmetry
see Key Stage 3 programme of study)
- find lines of reflection symmetry in shapes and diagrams
- recognise order of rotation symmetry
• transform shapes
- reflect shapes in oblique (45°) mirror lines where the shape either
does not touch the mirror line, or where the shape crosses the mirror
line
- reflect shapes not presented on grids, by measuring perpendicular
distances to/from the mirror
- reflect shapes in two mirror lines, where the shape is not parallel or
perpendicular to either mirror
- rotate shapes, through 90° or 180°, when the centre of rotation is a
vertex of the shape, and recognise such rotations
- translate shapes along an oblique line
• reason about shapes, positions and movements
- visualise a 3-D shape from its net and match vertices that will be
joined
- visualise where patterns drawn on a 3-D shape will occur on its net,
e.g. when shown a cube with patterns drawn on two or three faces,
create the net to make the cube
- draw shapes with a fixed number of lines of symmetry
• measure and draw angles to the nearest degree, when
constructing models and drawing or using shapes, e.g.
- measure and draw reflex angles to the nearest degree, when neither
edge is horizontal/vertical
- construct a triangle given the length of two sides and the angle
between them (accurate to 1 mm and 2°)
• use language associated with angle
• read and interpret scales on a range of measuring instruments,
explaining what each labelled division represents
• solve problems involving the conversion of units, e.g.
- solve problems such as 1.5 kg ÷ 30 g
- work out approximately how many km are equivalent to 20 miles
• make sensible estimates of a range of measures in relation to
everyday situations
• understand and use the formula for the area of a rectangle and
distinguish area from perimeter
- find the length of a rectangle given its perimeter and width
- find the area or perimeter of simple L shapes, given some edge
lengths